Factorizing multivariate function classes
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
A Linear Non-Gaussian Acyclic Model for Causal Discovery
The Journal of Machine Learning Research
Sparse Linear Identifiable Multivariate Modeling
The Journal of Machine Learning Research
Information-geometric approach to inferring causal directions
Artificial Intelligence
Pairwise likelihood ratios for estimation of non-Gaussian structural equation models
The Journal of Machine Learning Research
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By taking into account the nonlinear effect of the cause, the inner noise effect, and the measurement distortion effect in the observed variables, the post-nonlinear (PNL) causal model has demonstrated its excellent performance in distinguishing the cause from effect. However, its identifiability has not been properly addressed, and how to apply it in the case of more than two variables is also a problem. In this paper, we conduct a systematic investigation on its identifiability in the two-variable case. We show that this model is identifiable in most cases; by enumerating all possible situations in which the model is not identifiable, we provide sufficient conditions for its identifiability. Simulations are given to support the theoretical results. Moreover, in the case of more than two variables, we show that the whole causal structure can be found by applying the PNL causal model to each structure in the Markov equivalent class and testing if the disturbance is independent of the direct causes for each variable. In this way the exhaustive search over all possible causal structures is avoided.